MathDB

SAMO Problem 5: Sequence of integers with divisibility condition

Source: South African Mathematics Olympiad 2018, Problem 5

July 27, 2018

number theorySequencesDivisibility

Problem Statement

Determine all sequences

a_1, a_2, a_3, \dots

of nonnegative integers such that

a_1 < a_2 < a_3 < \dots

and

a_n

divides

a_{n - 1} + n

for all

n \geq 2